Robust heteroclinic cycles in delay differential equations

DOI10.1080/14689367.2010.500609zbMath1204.37053OpenAlexW1997777680MaRDI QIDQ3069827

Pietro-Luciano Buono

Publication date: 20 January 2011

Published in: Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/14689367.2010.500609

zbMATH Keywords

equivariancedelay-differential equationsheteroclinic cyclessymmetry-breaking bifurcationsrealization theorems

Mathematics Subject Classification ID

Dynamical aspects of symmetries, equivariant bifurcation theory (37G40) Bifurcation theory of functional-differential equations (34K18) Homoclinic and heteroclinic orbits for dynamical systems (37C29)

Related Items (1)

Coexistence of Hopf-Born rotation and heteroclinic cycling in a time-delayed three-gene auto-regulated and mutually-repressed core genetic regulation network

Cites Work

• Unnamed Item
• Robust heteroclinic cycles
• Heteroclinic cycles in rings of coupled cells
• Solving ODEs and DDEs with residual control
• Restrictions and unfolding of double Hopf bifurcation in functional differential equations
• Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation
• Normal forms for retarded functional differential equations and applications to Bogdanov-Takens singularity
• The Poincaré-Bendixson theorem for monotone cyclic feedback systems with delay
• Toroidal normal forms for bifurcations in retarded functional differential equations. I: Multiple Hopf and transcritical/multiple Hopf interaction
• Heteroclinic cycles between unstable attractors
• Experimental observation of near-heteroclinic cycles in the von Kármán swirling flow
• Structurally stable heteroclinic cycles
• The interaction of two spatially resonant patterns in thermal convection. Part 1. Exact 1:2 resonance
• Asymptotic stability of heteroclinic cycles in systems with symmetry
• CYCLING CHAOS
• Coupled cells with internal symmetry: I. Wreath products
• Asymptotic stability of heteroclinic cycles in systems with symmetry. II
• Heteroclinic cycles involving periodic solutions in mode interactions with O(2) symmetry
• Realisation of ordinary differential equations by retarded functional differential equations in neighbourhoods of equilibrium points
• Stability of genetic regulatory networks with time delay
• Unstable attractors: existence and robustness in networks of oscillators with delayed pulse coupling
• Solving DDEs in Matlab

This page was built for publication: Robust heteroclinic cycles in delay differential equations